Method for compensating for off-axis tilting of a lens

ABSTRACT

A method for compensating for off-axis tilting of a lens relative to an image sensor in an image acquisition device comprises acquiring a set of calibrated parameters 
               n   →     ≡     (           n   x               n   y               n   z           )           
corresponding to the tilting of said lens. P x ′ and P y ′ indicate a coordinate of a pixel in an acquired image. Image information is mapped from the acquired image to a lens tilt compensated image according to the formulae:
 
               P   x   ′     =       s       n   z     ⁡     (       n   z     -   1     )         ⁢     (         (       n   x   2     +       n   z     ⁡     (       n   z     -   1     )         )     ⁢     u   x       +       n   x     ⁢     n   y     ⁢     u   y         )                     P   y   ′     =       s       n   z     ⁡     (       n   z     -   1     )         ⁢     (         (       n   y   2     +       n   z     ⁡     (       n   z     -   1     )         )     ⁢     u   y       +       n   x     ⁢     n   y     ⁢     u   x         )             
where s comprises a scale factor given by
 
             s   =       n   z           u   x     ⁢     n   x       +       u   y     ⁢     n   y       +     n   z               
and where u x  and u y  indicate the location of a pixel in the lens tilt compensated image.

FIELD

The present invention relates to a method for compensating for off-axistilting of a lens.

BACKGROUND

Referring now to FIG. 1, when a lens is assembled to a camera, it ishard to ensure that an optical axis of the lens is perfectlyperpendicular to an imaging sensor surface. Unless compensation isapplied, this misalignment will cause geometrical distortion to anyimage produced by the lens.

In order to compensate for lens tilt, it must be properly modelled andthe modelling parameters estimated.

Both Matlab Camera Calibration Toolbox and OpenCV refer to thedistortion caused by lens tilt as “tangential distortion” and suggestthat it can be corrected by the following set of equations:x _(dist) =x+(2p ₁ xy+p ₂(r ²+2x ²))y _(dist) =Y+(p ₁(r ²+2y ²)+2p ₂ xy)

where x_(dist), y_(dist) are the x,y coordinates of a pixel within animage distorted by a tilted lens; x, y are the normalised pixelcoordinates;

r is the distance to the optical axis where r=√{square root over(x²+y²)}; and

p₁,p₂ are the modelling parameters.

However, according to Beauchemin et al., “Modelling and Removing Radialand Tangential Distortions in Spherical Lenses”, Multi-Image Analysis,10th International Workshop on Theoretical Foundations of ComputerVision Dagstuhl Castle, Germany, Mar. 12-17, 2000, pp. 1-21 the aboveequations are based on thin prism distortion caused by the misalignmentof the lens optical elements and are applicable only to sphericallenses. Thus, these equations may not be applicable in the case oflenses containing a large number of aspherical elements such as lensassemblies common in modern smartphones.

SUMMARY

There is provided an image acquisition system arranged to compensate foroff-axis tilting of a lens according to each of claim 1 or 4.

In an image acquisition system with a lens tilt of 0.25 degrees, theerrors between the present method and the conventional method are 1.5pixels on average with 3 pixels maximum for a 2 Mpixel Full-HD imagesensor. This error gets worse for higher resolutions and so theimprovement provided by the invention improves for higher resolutionimage sensors.

Similarly, the error grows quite significantly with the amount of tilt,thus lower quality lens modules can also benefit more from the inventionthan higher quality devices.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of example,with reference to the accompanying drawings, in which:

FIG. 1 shows lens projection on perpendicular and on tilted projectionplanes;

FIG. 2 illustrates an image acquisition system arranged to compensatefor off-axis tilting of a lens according to the present invention;

FIG. 3 shows vectors describing projection on a tilted plane employed indescribing an embodiment of the present invention;

FIG. 4A and FIG. 4B show conic sections employed in a second approach todescribing an embodiment of the present invention;

FIG. 5 illustrates the conic section and vectors of FIG. 4A and FIG. 4B;and

FIG. 6 shows a non-linear mapping {right arrow over (p)}

{right arrow over (q)} projecting the coordinates of a circle onto anellipse according to the present invention.

DESCRIPTION OF THE EMBODIMENTS

Referring now to FIG. 2 an image acquisition system 200 according to anembodiment of the present invention is shown. The acquisition system 200comprises an otherwise conventional lens system 20 and sensor 22assembly where the optical axis of the lens may not be orthogonal to thesensor surface. The lens 20 may either be integrally formed within theacquisition system 200, as in the case of smartphones, tablets or laptopcomputers and indeed some dedicated cameras; or the lens 20 may be ofthe interchangeable type fitted to a camera body. Typically, raw imageinformation acquired by the sensor 22 is initially processed by an imagesensor pipeline (ISP) 24 before an image 32 is written across a systembus 28 for storage in system memory 30.

Compensation for lens tilt can be implemented at any stage in the imageprocessing pipeline and in the example of FIG. 2, a compensation module26 is shown downstream in the image processing pipeline from the ISP 24.The module functionality may of course be integrated with the ISP 24 orindeed any other module processing acquired image information before itis written to system memory, for example, a module performing otherforms of distortion correction as described in U.S. Pat. No. 9,280,810and U.S. patent application Ser. No. 15/879,310, the disclosure of whichare herein incorporated by reference. Alternatively, the module might beapplied as part of a post-processing of an image 32 stored in memory 30and could be implemented either as dedicated firmware, as described inthe above referenced U.S. Pat. No. 9,280,810 and U.S. patent applicationSer. No. 15/879,310, or in software running on a general purposeprocessor such as a system controller 34 for the system 200.

In any case, the system controller 34 provides the compensation module26 with a set of parameters {right arrow over (n)} which can then beused by the module 26 to map pixel information from an image distortedby lens tilt to a distortion corrected image and these parameters alongwith how they can be used are described in more detail below.

In the description below, the effect caused by lens tilt does not needto take into account lens projection, as the model is only concernedwith the path of light exiting the lens 20.

It can be observed, that for any field angle, the lens is producing acone of light that intersects the sensor surface. We need to find theshape of the intersection as a function of the tilt. It is convenient todescribe such a transformation in terms of mapping the “perfect” pointcoordinates produced by the lens 20 when it is perfectly aligned withthe sensor 22, to the new coordinates which are distorted by the sensortilt. In this way, the lens projection characteristics can be separatedfrom the effect caused by the lens tilt. The problem can be approachedfrom two directions, each producing equivalent end results:

1. Modelling the Lens Tilt by Raytracing

For convenience, we can assume that a projection plane is on the sameside of the plane as object. It is a common convention used in computergraphics as the ISP 24 typically flips the raw image produced by lens20, so there is no point in reversing this process in order to model thefact that the lens produces a flipped image.

We adopt the convention that the z-axis of the coordinate system is theoptical axis and the ideal projection (not tilted) is done on the planez=1 with the projection centre in the origin of the coordinate system.

Referring now to FIG. 3 which comprises a sideways view on the xz plane,let S0 be the horizontal sensor plane and S1 the tilted sensor plane.The normal vector of S0 will be:

$\overset{\rightarrow}{w} \equiv \begin{pmatrix}0 \\0 \\{- 1}\end{pmatrix}$

and the unit normal vector of S1 will be

$\overset{\rightarrow}{n} \equiv \begin{pmatrix}n_{x} \\n_{y} \\n_{z}\end{pmatrix}$

An ideally projected point will form a vector

$\overset{\rightarrow}{u} \equiv \begin{pmatrix}u_{x} \\u_{y} \\1\end{pmatrix}$

where u_(x) and u_(y) are normalised coordinates on the horizontal planeS0.

The first stage of this approach is to find a point {right arrow over(P)} which is the intersection of the ray described by the vector {rightarrow over (u)} with the plane S1. In order to do that we need to find ascale factor s that will stretch the vector {right arrow over (u)} tomake it meet with S1. The scale factor s is defined as:

$s = {- \frac{\overset{\rightarrow}{n} \cdot \overset{\rightarrow}{w}}{\overset{\rightarrow}{n} \cdot \overset{\rightarrow}{u}}}$

Since the vector {right arrow over (w)} is aligned with the coordinatesystem it can be simplified to:

$s = \frac{n_{z}}{{u_{x}n_{x}} + {u_{y}n_{y}} + n_{z}}$

The 3D position of the point {right arrow over (P)} is defined as

$\overset{\rightarrow}{P} = {\begin{pmatrix}P_{x} \\P_{y} \\P_{z}\end{pmatrix} = {{s\overset{\rightarrow}{u}} = {s\begin{pmatrix}u_{x} \\u_{y} \\1\end{pmatrix}}}}$

These calculations are relatively simple to implement and are veryfriendly for GPU or DSP implementations where dot products can beefficiently calculated by using SIMD (Single Instruction/Multiple Data)instructions.

Since we are interested in the position of point {right arrow over (P)}in the local coordinates of S1, the coordinates of point {right arrowover (P)} must be rotated in order to align them with the xy plane ofthe coordinate system. This can be done by finding a rotation matrix{circumflex over (R)} that rotates the vector {right arrow over (n)} tothe vector {right arrow over (w)}.

The rotation axis is defined by the cross product between the vectors{right arrow over (n)} and {right arrow over (w)}:

$\overset{\rightarrow}{v} = {{\overset{\rightarrow}{n} \times \overset{\rightarrow}{w}} = \begin{pmatrix}{- n_{y}} \\n_{x} \\0\end{pmatrix}}$ $\overset{\rightarrow}{v} = {\begin{pmatrix}v_{x} \\v_{y} \\v_{z}\end{pmatrix} = \begin{pmatrix}{- n_{y}} \\n_{x} \\0\end{pmatrix}}$

and the cosine of the rotation angle is defined as the dot productbetween these vectors:cos θ={right arrow over (w)}·{right arrow over (n)}=−n _(z)

The vector {right arrow over (v)} can be used to construct askew-symmetric matrix {circumflex over (V)}:

$\hat{V} = \begin{bmatrix}0 & {- v_{z}} & v_{y} \\v_{z} & 0 & {- v_{x}} \\{- v_{y}} & v_{x} & 0\end{bmatrix}$

The rotation matrix {circumflex over (R)} can be calculated byrearranging the Rodriguez formula to the following form, and plugging infor the values of cos θ and {circumflex over (V)}:

$\hat{R} = {{+ \hat{V} + \frac{{\hat{V}}^{2}}{1 + {\cos\;\theta}}} = \begin{bmatrix}{1 + \frac{n_{x}^{2}}{n_{z} - 1}} & \frac{n_{x}n_{y}}{n_{z} - 1} & n_{x} \\\frac{n_{x}n_{y}}{n_{z} - 1} & {1 + \frac{n_{y}^{2}}{n_{z} - 1}} & n_{y} \\{- n_{x}} & {- n_{y}} & {- n_{z}}\end{bmatrix}}$

To perform the rotation around the projection plane origin, the pointshave to be first shifted to the coordinate centre, rotated then shiftedback to the original location. So the final point coordinates in thelocal coordinate system of the tilted plane are defined as follows:{right arrow over (P)}′={circumflex over (R)}({right arrow over(P)}+{right arrow over (w)})−{right arrow over (w)}

Since we are not interested in the z coordinate of the point {rightarrow over (P)}′ (as it should equal 1 for all points), the calculationscan be simplified to:

$P_{x}^{\prime} = {\frac{s}{n_{z}\left( {n_{z} - 1} \right)}\left( {{\left( {n_{x}^{2} + {n_{z}\left( {n_{z} - 1} \right)}} \right)u_{x}} + {n_{x}n_{y}u_{y}}} \right)}$$P_{y}^{\prime} = {\frac{s}{n_{z}\left( {n_{z} - 1} \right)}\left( {{\left( {n_{y}^{2} + {n_{z}\left( {n_{z} - 1} \right)}} \right)u_{y}} + {n_{x}n_{y}u_{x}}} \right)}$

with the scale factors given by

$s = \frac{n_{z}}{{u_{x}n_{x}} + {u_{y}n_{y}} + n_{z}}$

The form of the above equations makes them readily computed using SIMDinstructions. For example, the compensation module 26 can simply stepthrough each u_(x), u_(y) pixel location of a lens tilt compensatedoutput image and determine the corresponding coordinates P_(x)′, P_(y)′in the input distorted image—note that these coordinates need notnecessarily correspond with a pixel location in the input image. Asdescribed in U.S. Pat. No. 9,280,810 and U.S. patent application Ser.No. 15/879,310, some interpolation between input image pixel values forpixel locations surrounding the input image coordinates may then berequired to produce the pixel value for the output image pixel location.

Moreover, slight reorganisation of the equations will allow for furtherparallelization. The calculation of s and the expression in parenthesescan be performed in parallel followed by the multiplication of theresults.

2. Modelling the Lens Tilt by Conical Section

Referring to FIG. 4A and FIG. 4B which show conic sections employed in asecond approach to describing an embodiment of the present invention.

The circle 10 shows the intersection between the horizontal plane S0 andthe cone of light 11 produced by the lens that intersects the sensorsurface; the ellipse 12 is the intersection of the tilted plane S1 andthe cone; and the ellipse 14 is the ellipse after rotation back to thehorizontal plane S0. A non-linear mapping {right arrow over (p)}

{right arrow over (q)}, FIG. 6, detailed below transforms the points ofthe circle 10, to the ellipse 14.

In this case, the coordinate system is inverted with respect to theprevious ray tracing approach, as the optical centre is located at(0,0,1), so the focal point vector {right arrow over (f)}=−{right arrowover (w)}, and the horizontal plane is located at z=0.

Referring to FIG. 5, if {right arrow over (n)} is a normal vector to theplane Z, the general equation of the plane is given by the set of allpoints {right arrow over (z)}∈Z which satisfy:{right arrow over (n)}·{right arrow over (z)}=xn _(x) +yn _(y) +zn _(z)+n ₁=0

and the vectors are:

$\overset{\rightarrow}{z} = \begin{pmatrix}x \\y \\z \\1\end{pmatrix}$ $\overset{\rightarrow}{n} = \begin{pmatrix}n_{x} \\n_{y} \\n_{z} \\n_{1}\end{pmatrix}$

where {right arrow over (z)} is an element of the 3-dimensionalprojective plane {right arrow over (z)}∈

³. The 4^(th) element of the normal vector is a translational componentand describes the displacement of the tilted plane from the origin:(x,y,z)=(0,0,0). Here we need only consider planes which contain theorigin. Therefore we may exclude the translational component and treatthe unit normal {right arrow over (n)} as a 3-vector. There are 2 planesthat are of interest to this study; respectively defined by the normalvectors

-   -   Horizontal plane:

${\overset{\rightarrow}{n}}_{0} \equiv \begin{pmatrix}0 \\0 \\1\end{pmatrix}$

-   -   Tilted plane:

${\overset{\rightarrow}{n}}_{1} \equiv \begin{pmatrix}n_{x} \\n_{y} \\n_{z}\end{pmatrix}$

With {right arrow over (n)}₀={right arrow over (f)}, which is the focalpoint {right arrow over (f)} of the lens, and the centre of projection.

$\overset{\rightarrow}{f} = \begin{pmatrix}0 \\0 \\1\end{pmatrix}$

The cone of light rays 11 emanating from the focal point is illustratedin FIG. 4A. For a given field angle, the lens is producing a cone oflight that intersects the imaging sensor. In the ideal case the imagingsensor is perfectly perpendicular to the optical axis and theintersection points describe a circle 10.

The 2-dimensional coordinates of the intersection points with thehorizontal plane are described by the vector:

$\overset{\rightarrow}{p} = \begin{pmatrix}p_{x} \\p_{y} \\0\end{pmatrix}$

The light rays extend from the centre of projection toward thehorizontal plane.

$\overset{\rightarrow}{l} = {{\overset{\rightarrow}{p} - \overset{\rightarrow}{f}} = \begin{pmatrix}p_{x} \\p_{y} \\{- 1}\end{pmatrix}}$

The light rays {right arrow over (l)} extend from the focal point {rightarrow over (f)} and intersect the horizontal plane at {right arrow over(p)}. The intersection points are transformed to the tilted plane {rightarrow over (q)}₀ under the non-linear mapping{right arrow over (p)}

{right arrow over (q)} ₀

Where {right arrow over (q)}₀ are the 3-dimensional transformedcoordinates defined by{right arrow over (q)} ₀ ={right arrow over (f)}+λ{right arrow over (l)}

Where is the non-linear scaling of the light rays between the horizontaland tilted plane. The explicit form of the scaling parameter is foundfrom the dot product of {right arrow over (q)}₀ with the normal to thetilted imaging sensor plane {right arrow over (n)}.

${\overset{\rightarrow}{n} \cdot \left( {\overset{\rightarrow}{f} + {\lambda\;\overset{\rightarrow}{l}}} \right)} = 0$$\lambda = {- \frac{\overset{\rightarrow}{n} \cdot \overset{\rightarrow}{f}}{\overset{\rightarrow}{n} \cdot \overset{\rightarrow}{l}}}$$\lambda = \frac{n_{z}}{n_{z} - {n_{x}p_{x}} - {n_{y}p_{y}}}$

The light rays intersect the tilted plane at {right arrow over (q)}₀.

${\overset{\rightarrow}{q}}_{0} = \begin{pmatrix}{\lambda\; p_{x}} \\{\lambda\; p_{y}} \\{1 - \lambda}\end{pmatrix}$

The intersection of the light rays with the tilted plane is illustratedby the ellipse 12 in FIG. 4A, FIG. 4B, and FIG. 5. When the imagingsensor 22 is tilted with respect to the optical axis, it is rotated byan angle θ around an axis {right arrow over (k)} which passes throughthe origin. The rotation axis is the cross product of the focal pointvector {right arrow over (f)} and the unit normal {right arrow over(n)}.

$\overset{\rightarrow}{k} = {\overset{\rightarrow}{f} \times \overset{\rightarrow}{n}}$$\overset{\rightarrow}{k} = {\begin{pmatrix}k_{x} \\k_{y} \\k_{z}\end{pmatrix} = \begin{pmatrix}n_{y} \\{- n_{x}} \\0\end{pmatrix}}$

The cosine of the angle of rotation is given by the dot product betweenthe unit normal to the tilted plane and the focal point vector:cos θ={right arrow over (f)}·{right arrow over (n)}=n _(z)

We seek the non-linear mapping:{right arrow over (p)}

{right arrow over (q)}

Where {right arrow over (p)} and {right arrow over (q)} are2-dimensional vectors, both with a zero component along the optical axisp_(z)=q_(z)=0.

The 2-dimensional transformed coordinates are found by rotating {rightarrow over (q)}₀ back to the horizontal plane, via:{right arrow over (q)}={circumflex over (Q)}{right arrow over (q)} ₀

{circumflex over (Q)} is an axis-angle quaternion, described by theRodrigues rotation equation.

$\hat{Q} = {+ \hat{K} + {{\hat{K}}^{2}\left( \frac{1}{1 + {\cos\;\theta}} \right)}}$

where

is the identity matrix, and {circumflex over (K)} is a skew symmetricmatrix given by the axis of rotation:

$\hat{K} = \begin{bmatrix}0 & {- k_{z}} & k_{y} \\k_{z} & 0 & {- k_{x}} \\{- k_{y}} & k_{x} & 0\end{bmatrix}$

Making the substitutionscos θ=n _(z) and (k _(x) ,k _(y) ,k _(z))=(n _(y) ,−n _(x),θ)

the Rodrigues axis-angle quaternion simplifies to:

$\hat{Q} = \begin{bmatrix}{1 - \frac{n_{x}^{2}}{1 + n_{z}}} & {- \frac{n_{x}n_{y}}{1 + n_{z}}} & {- n_{x}} \\{- \frac{n_{x}n_{y}}{1 + n_{z}}} & {1 - \frac{n_{y}^{2}}{1 + n_{z}}} & {- n_{y}} \\n_{x} & n_{y} & n_{z}\end{bmatrix}$

Applying the rotation{right arrow over (q)}={circumflex over (Q)}{right arrow over (q)} ₀

we obtain the 2-dimensional transformed coordinates

$\overset{\rightarrow}{q} = {\frac{\lambda}{n_{z}\left( {1 + n_{z}} \right)}\begin{pmatrix}{{\left( {n_{x}^{2} + {n_{z}\left( {1 + n_{z}} \right)}} \right)p_{x}} + {n_{x}n_{y}p_{y}}} \\{{\left( {n_{y}^{2} + {n_{z}\left( {1 + n_{z}} \right)}} \right)p_{y}} + {n_{x}n_{y}p_{x}}} \\0\end{pmatrix}}$

The non-linear mapping from p_(x)

q_(x), and from p_(y)

q_(y), is

$\left. p_{x}\mapsto{\frac{\lambda}{n_{z}\left( {1 + n_{z}} \right)}\left( {{\left( {n_{x}^{2} + {n_{z}\left( {1 + n_{z}} \right)}} \right)p_{x}} + {n_{x}n_{y}p_{y}}} \right)} \right.$$\left. p_{y}\mapsto{\frac{\lambda}{n_{z}\left( {1 + n_{z}} \right)}\left( {{\left( {n_{y}^{2} + {n_{z}\left( {1 + n_{z}} \right)}} \right)p_{y}} + {n_{x}n_{y}p_{x}}} \right)} \right.$

with the scale factor λ given by:

$\lambda = \frac{n_{z}}{n_{z} - {n_{x}p_{x}} - {n_{y}p_{y}}}$

Now that the parameters {right arrow over (n)} defining the abovedescribed model and their application to compensate an acquired imagefor lens tilt have been described, it will be appreciated that any imageacquisition system 200 (camera) having a lens tilt calibration module 26driven by these parameters {right arrow over (n)} can be readilycalibrated as described at the following link:http://ags.cs.uni-kl.de/fileadmin/inf ags/3dcv-ws11-12/3DCV WS11-12lec03.pdf, Stricker by pointing the camera at a 3-surface referenceobject to acquire a single 2-D image and then applying a globaloptimisation algorithm to determine parameters both for camera location(X,Y,Z) and rotation (Rx,Ry,Rz) relative to the reference object as wellas camera model parameters including taking into account lens distortionas well as lens tilt parameters {right arrow over (n)} by minimizing anerror function mapping the points of the reference object to locationsin the acquired 2-D image.

While the approach of Stricker is based on a reference object includinga checkerboard type pattern, other reference objects can comprisesurfaces including boards comprising unique ChArUco characters ratherthan a repeating pattern of the same unit.

Note that there may also be a loss in focus associated with lens tiltbut this is not considered in detail here. Nonetheless, the abovecompensation technique can be combined with any other techniquecompensating for any loss of focus.

In variants of the above embodiments, rather than supplying the threecoordinates for the vector {right arrow over (n)} directly, these caninstead be derived from a pair of scalars, NX and NY generated by acalibration process as described above. First, a length of the inputvector is calculated as follows: d=sqrt(NX²+NY²+1) (essentially a thirdscalar NZ=1). Then the components of the vector {right arrow over (n)}are calculated as follows:n _(x) =NX/dn _(y) =NY/dn _(z)=1/d.

Using such an approach, the interface for the compensation module 26 canbe made interchangeable with that of compensation modules using theprior art approach, yet still provide an improved result.

Note that the above derivation from two parameters is just an exampleand other methods might be used, for example, the vector {right arrowover (n)} could be derived from two rotation angles of a sensor plane.

The invention claimed is:
 1. An image acquisition system comprising alens assembled to project an image onto an image sensor, where the lensis tilted relative to the image sensor, the image acquisition systemincluding a calibration module configured to: acquire a set ofcalibrated parameters $\overset{\rightarrow}{n} \equiv \begin{pmatrix}n_{x} \\n_{y} \\n_{z}\end{pmatrix}$  corresponding to said tilting of said lens, where z isthe optical axis relative to which said lens is tilted; acquire an imagefrom said image sensor through said lens, where P_(x)′ and P_(y)′indicate a coordinate of a pixel in said acquired image; map imageinformation from said acquired image to a lens tilt compensated imageaccording to the formulae:$P_{x}^{\prime} = {\frac{s}{n_{z}\left( {n_{z} - 1} \right)}\left( {{\left( {n_{x}^{2} + {n_{z}\left( {n_{z} - 1} \right)}} \right)u_{x}} + {n_{x}n_{y}u_{y}}} \right)}$${P_{x}^{\prime} = {\frac{s}{n_{z}\left( {n_{z} - 1} \right)}\left( {{\left( {n_{x}^{2} + {n_{z}\left( {n_{z} - 1} \right)}} \right)u_{x}} + {n_{x}n_{y}u_{y}}} \right)}}\;$where s comprises a scale factor given by$s = \frac{n_{z}}{{u_{x}n_{x}} + {u_{y}n_{y}} + n_{z}}$ and where u_(x)and u_(y) indicate the location of a pixel in said lens tilt compensatedimage; and store said lens tilt compensated image in a memory.
 2. Animage acquisition system according to claim 1 wherein said calibrationmodule is configured to map image information by: selecting a pixellocation u_(x), u_(y) in said lens tilt compensated image, determining acorresponding coordinate P_(x)′, P_(y)′ in said acquired image,determining a plurality of pixel locations in said acquired imagesurrounding said coordinate, and interpolating pixel values for saidsurrounding pixel locations to determine a value for the pixel locationin said lens tilt compensated image.
 3. An image acquisition systemaccording to claim 1 wherein said calibration module is configured toacquire said set of calibrated parameters$\overset{\rightarrow}{n} \equiv \begin{pmatrix}n_{x} \\n_{y} \\n_{z}\end{pmatrix}$ by: acquiring a pair of calibrated scalar parameters NX,NY; determining a length d=sqrt(NX²+NY²+1); and calculating thecomponents of {right arrow over (n)} as follows:n _(x) =NX/dn _(y) =NY/dn _(z)=1/d.
 4. An image acquisition system comprising a lens assembledto proiect an image onto an image sensor, while the lens is tiltedrelative to the image sensor, the image acquisition system including acalibration module configured to: acquire a set of calibrated parameters$\overset{\rightarrow}{n} \equiv \begin{pmatrix}n_{x} \\n_{y} \\n_{z}\end{pmatrix}$  corresponding to said tilting of said lens, where z isthe optical axis relative to which said lens is tilted; acquire an imagefrom said image sensor through said lens, where p_(x) and p_(y) indicatea location of a pixel in a lens tilt compensated image; map imageinformation from said lens tilt compensated image to said acquired imageaccording to the formulae:$\left. p_{x}\mapsto{\frac{\lambda}{n_{z}\left( {1 + n_{z}} \right)}\left( {{\left( {n_{x}^{2} + {n_{z}\left( {1 + n_{z}} \right)}} \right)p_{x}} + {n_{x}n_{y}p_{y}}} \right)} \right.$$\left. p_{y}\mapsto{\frac{\lambda}{n_{z}\left( {1 + n_{z}} \right)}\left( {{\left( {n_{y}^{2} + {n_{z}\left( {1 + n_{z}} \right)}} \right)p_{y}} + {n_{x}n_{y}p_{x}}} \right)} \right.$where λ comprises a scale factor given by:${\lambda = \frac{n_{z}}{n_{z} - {n_{x}p_{x}} - {n_{y}p_{y}}}};$ andstore said lens tilt compensated image in a memory.
 5. An imageacquisition system according to claim 4 wherein said calibration moduleis configured to map image information by: selecting a pixel locationp_(x), p_(y) in said lens tilt compensated image, determining acorresponding coordinate in said acquired image, determining a pluralityof pixel locations in said acquired image surrounding said coordinate,and interpolating pixel values for said surrounding pixel locations todetermine a value for the pixel location in said lens tilt compensatedimage.
 6. An image acquisition system according to claim 4 wherein saidcalibration module is configured to acquire said set of calibratedparameters $\overset{\rightarrow}{n} \equiv \begin{pmatrix}n_{x} \\n_{y} \\n_{z}\end{pmatrix}$ by: acquiring a pair of calibrated scalar parameters NX,NY; determining a length d=sqrt(NX²+NY²+1); and calculating thecomponents of {right arrow over (n)} as follows:n _(x) =NX/dn _(y) =NY/dn _(z)=1/d.